This started as a slip of the tongue, a mangled idiom, but it led me on a journey of discovery.
New Zealanders, perhaps like Canadians, have a high bar when it comes to being polite. Like most things this has pros and cons. One big problem with being polite to a fault is failing to communicate critical evaluations to others.
Paul Graham has an article about differing levels of disagreement and the corresponding weight with which those arguments can be viewed. This should be obvious to any student of critical thinking or logic.
‘Begging to differ’ is the common idiomatic form and is defined as disagreeing politely. I would submit this is a valuable and learnable skill that is most certainly worthy of development.